Occupation / queue size

1
Occupation / queue size
D/D/1 Constant arrivals, constant
duration. M/D/1 Exponential arrivals, constant
duration.
queue size
4a
2a
a
occupation rate
0.6
0.8
0.9
1
2
Arena experiments
M/D/1 queues.
D/D/1 queues.
Tandem queues.
3
Assignment 2
Goal obtain Arena knowledge. Modelingexperimenti
ng.
Various models are possible. Several modeling
pitfalls.
Use of expression builder. Repeated test vs.
"hold" block.
4
Modeling parameter choice
Problem definition
Conceptual impl Arena CPN Tools
Modeling
parameterization
Validation
Experiment
Interpret
5
Modeling parameters
Parameters for a model obtained by a combination
of
- observations (direct / video recordings),
- event logs (e.g. SAP) often interpretation
needed,
- interviews.
Select a distribution that accords with
theory and matches measured averages. Example
"create" block M measured arrivals in N time
units exponential distribution with intensity M
/ N.
6
DCT arrivals
Import trace into spreadsheet.
DCT trace arrival 1 at 0.00, 500 at
687.835. exp., avg interarrival time 687.835 /
499.
Model should differentiate between B/F/BF
trucks three generators with three different
intensities.
Intensities may stay the same or fluctuate. first
108 B trucks 0-265, next 108 265-678 first 49 BF
trucks 13-363, next 49 368-681 first 90 F trucks
1-427, next 90 427-686. There may be reasons for
fluctuations (e.g. traffic) look for
confirmation by interviews!
7
Arena input analyzer
Trace file is imported into spreadsheet and
sorted. Export selected data to text file, which
can be read by input analyzer.
Example with interarrival times for B
trucks. However, no variable-intensity
exponential distribution. So, divide in subparts
and analyze separately. Keep asking
questions! Listen to answers given!
8
Processing times
Inferring processing times from trace. Problem
with assessing duration for steps
needing resources. Suppose step needs a resource
R.
Job id start B rdy B 123 8.79 10.01 127 11
.26 13.10 136 13.24 14.67 132 14.87 16.25
Idle time of R in between? Look at predecessor
job(s)!
9
Assess resource occupation
Job id rdy A start B rdy B 123 8.58
8.79 10.01 127 11.13 11.26 13.10 136 12.09 1
3.24 14.67 132 13.12 14.87 16.25
When is resource R idle?
Apparently, R not immediately available after rdy
B.
10
Resource usage modeling
Job id rdy A start B rdy B 123 8.58
8.79 10.01 127 11.13 11.26 13.10 136 12.09 1
3.24 14.67 132 13.12 14.87 16.25
A2B
st B
rdy B
rdy A
B-queue empty ? t can be timed ? u cannot be
timed
11
DCT processing
Important for keeper occupation arrival (ar),
start (sk), error (er), approved (ap), fail (fl).
ar sk er ap fl
31.84 34.70 - 37.32 -
34.85 37.42 39.49 - 44.70
35.42 39.55 - 40.79 -

47.33 56.06 - 56.78 -
47.68 56.85 58.26 63.31 -
47.89 58.31 - 59.11 -
50.33 59.16 - 61.19 -
51.84 63.40 - 64.33 -
extra keeper occupation
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Keeper process
Keeper busy time(ap) - time(sk) plm. 0.07 if
OK time(er) - time(sk) plm. 0.07 if failure
time(er) - time(sk) ?(extra) if corrected
Assumption extra time equals normal check time
13
DCT processing
Important for crane occupation mv/d, s1/2, gt/p,
pt/p, rd.
ap mv gt mv rd pp
23.70 - 24.19 24.38 24.38 24.84
25.52 - 27.29 27.50 27.50 27.93
28.41 - 30.77 30.94 30.94 31.30
29.00 31.53 32.06 32.29 32.29 32.93
19(B)
21(B)
24(B)
0.23
25(B)
0.21
0.19
20(BF)
ap mv gt mv gt pp md s1 gp mv pt rd
24.36 25.05 25.33 25.05 25.33 25.94 26.16 26.31 26.44 26.68 27.10 27.28
ap mv md s2 gp mv pt rd
22(F)
26.22 - 28.12 - 28.27 28.47 28.86 29.10
23(F)
26.89 29.11 - 29.60 29.80 29.98 30.53 30.75
14
Crane process
Six different paths B, F, BF, with and without
extra first move. F and BF have an optional s1/s2
step for obtaining the needed container.
Two modeling options 1. Model each step fit
distributions for each step. Do not forget
the extra time after "pp" step. 2. Aggregate and
use a bit of analysis to approximate
distribution(s).
Simulation can be used to find out whether option
2 is appropriate.